A197809 Decimal expansion of x<0 having x^2+x=2*cos(x).

1, 3, 4, 0, 5, 2, 5, 3, 0, 8, 1, 9, 7, 3, 9, 8, 4, 4, 7, 8, 6, 7, 6, 0, 6, 2, 8, 4, 9, 9, 6, 0, 6, 6, 0, 9, 2, 0, 5, 8, 3, 4, 1, 8, 6, 8, 9, 3, 1, 2, 0, 4, 5, 7, 5, 5, 2, 4, 7, 3, 5, 7, 7, 3, 0, 0, 2, 1, 3, 0, 7, 8, 1, 3, 0, 4, 2, 1, 6, 6, 7, 3, 0, 3, 4, 7, 6, 9, 9, 7, 5, 6, 5, 9, 9, 9, 0, 8, 2

Offset: 1

Author

Clark Kimberling, Oct 20 2011

Keywords

• nonn
• cons

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			negative: -1.3405253081973984478676062849960660920583...
positive:  0.7883968459929654290788209839820019122955...
		

Crossrefs

Cf. A197738.

Programs

Mathematica

a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1.5}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.3}, WorkingPrecision -> 110]
RealDigits[r1] (* A197809 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .78, .79}, WorkingPrecision -> 110]
RealDigits[r2] (* A197810 *)